An image of Earth as a billiard ball. Despite claimed by many reputable sources, the idea of Earth being as smooth as a billiard ball is a myth.

No, Earth is NOT As Smooth As a Billiard Ball! [Here’s Why]

You may have heard it has been said that if the Earth were shrunk down to the size of a billiard ball, it would be smoother than it. In other words, the Earth is smoother than a billiard ball. Is that true?

It’s not. And I’ll explain why.

Back in 2008, on the “Bad Astronomy” blog on discovermagazine.com, in the article titled “Ten things you don’t know about the Earth“, Phil Plait wrote about that and said “…according to the World Pool-Billiard Association, a pool ball is 2.25 inches in diameter and has a tolerance of +/- 0.005 inches.” and after making some calculations, he concluded that “… the urban legend is correct. If you shrank the Earth down to the size of a billiard ball, it would be smoother.”

Even the famous American astrophysicist, author, and science communicator Neil deGrasse Tyson once tweeted about that, saying “If shrunk to a few inches across, Earth would feel as smooth as a billiard-hall cue ball.”. (You can see his tweet here)

Neil deGrasse Tyson tweet about the idea of Earth being as smooth as a billiard ball
Is Earth as smooth as a billiard ball? As I’ll explain shortly, no, it’s not. Incredibly, Mr. Neil deGrasse Tyson is still selling this nonsense.

Smoothness vs roundness

The Earth is much smoother than one might think. It definitely would NOT look like this without water, for example. Yes, there are big mountains like the Himalayas and big trenches under the oceans like the Mariana Trench, but despite these extreme points, our planet is really smooth. But is it really as smooth as a billiard ball?

The highest point on Earth is the top of Mount Everest, at 8.85 km. The deepest point on Earth is the Mariana Trench, at about 11 km deep. But even those are very small compared to the Earth’s diameter which is about 12,735 kilometers (on average).

According to the World Pool-Billiard Association:

“All balls must be composed of cast phenolic resin plastic and measure 2 1/4 (±.005) inches [5.715 cm (± .127 mm)] in diameter”.

World Pool-Billiard Association

If we could shrink the Earth to the size of a billiard ball, the height of Mount Everest would be only 0.04 millimeters. The depth of the Mariana Trench would be only 0.045 millimeters. These measurements are inside the tolerance of 0.127 mm or 0.005 inches, with no pits or bumps more than that, so the Earth is smoother than a billiard ball, right?

Wrong.

First of all, the specifications of the World Pool-Billiard Association do not say “There mustn’t be pits or bumps more than .005 inches”. This is only about diameter, the rule says that “the diameter must be within 2 1/4 (± .005) inches”.

Smoothness is a very different thing.

Let’s assume that we produced a billiard ball and covered its surface with a medium sandpaper (grit particle size of 0.005 inches – for more about grit sizes of sandpaper see the Grit size table on the Wikipedia entry of sandpaper).

By the definition of smoothness used by Phil Plait of Discover Magazine and Neil deGrasse Tyson, that billiard ball would also be “smooth” – which is ridiculous for obvious reasons.

The billiard-ball-sized Earth’s smoothness would be equivalent to that of 320-grit sandpaper. Still not quite smooth, right?

So, it’s obvious that 0.005 inches (0.127 mm) official tolerance is for shape, for roundness, not for smoothness.

The billiard-ball-sized Earth's smoothness would be equivalent to that of 320-grit sandpaper. Not quite smooth, right? Image: 320 grit silicon carbide sandpaper, with a close-up view on Wikipedia
The billiard-ball-sized Earth’s smoothness would be equivalent to that of 320-grit sandpaper. Not quite “smooth”, right? Image: “320 grit silicon carbide sandpaper, with a close-up view” on Wikipedia

Human fingertips are very sensitive

According to a 2013 study titled “Feeling Small: Exploring the Tactile Perception Limits” published in Nature, a human finger can feel wrinkles as small as 10nm (nanometers), or 0.00001 millimeters, demonstrating that human tactile discrimination extends to the nanoscale.

So, if the Earth were shrunk down to the size of a billiard ball, you would definitely feel Mount Everest, which would be 0.04 millimeters high. You could also feel most of the high mountains in the world.

Why Earth is not as smooth as a billiard ball? Dr. James O’Donoghue’s explanation

JAXA (Japan Aerospace Exploration Agency) scientist Dr. James O’Donoghue also tweeted about why Earth is not as smooth as a billiard ball. You can see the thread here.

Dr. James O’Donoghue uses the bowling ball to scale, but what he says is still valid for the billiard ball.

How smooth is Earth?

Earth’s highest/lowest points are 8.9 km (Mount Everest)/-11 km (Mariana Trench), but let’s assume a local variability of 1 km for now.

If Earth were shrunk to bowling-ball width (21.6 cm), then 1 km bumps represent 0.017 mm: about the particle size of P1000 superfine sandpaper!

If you thought 1km was too much variability, try 0.5km: P2500 Ultrafine sandpaper, particle size 0.0084mm

Mount Everest is 8.9 km above sea level and would be about half the size of a grain of salt (0.15 mm) at the scale of this bowling ball, albeit with a wide base.

So, perhaps Earth isn’t as smooth as a brand-new glossy bowling ball, but it’s not very rough either.

Something to end on: Earth’s oceans would be one-third the height of a grain of salt on the scale of a bowling ball, a film so thin your hands would barely get wet holding it.

Earth is as round as a billiard ball [but still it would make a terrible billiard ball]

Speaking of roundness, is Earth as round as a billiard ball?

Earth’s equatorial diameter is 7,926 miles (12,756 km), but from pole to pole, the diameter is 7,898 miles (12,714 km) – a difference of only 28 miles (42 km).

If we take the bigger diameter and shrink it down, the difference would be 0.0049 inches (0.0125 mm). If we take the smaller diameter, the difference would be very slightly bigger, but almost the same. So yes, the Earth is as round as a billiard ball. But it’s almost at the limit.

Dr. David Alciatore, Ph.D., writes:

“The Earth would make a terrible pool ball. Not only would it have a few extreme peaks and trenches still larger than typical pool-ball surface features, but the shrunken-Earth ball would also be terribly non-round compared to high-quality pool balls.”

“The diameter at the equator (which is larger due to the rotation of the Earth) is 27 miles greater than the diameter at the poles. That would correspond to a pool ball diameter variance of about 7 thousandths of an inch. Typical new and high-quality pool balls are much rounder than that, usually within 1 thousandth of an inch.”

Summary

  1. Is Earth as smooth as a billiard ball? Answer: No.
  2. Is Earth as round as a billiard ball? Answer: Yes, it is within the limits, but still it would make a terrible, terrible billiard ball.

You can also watch Vsauce’s great video titled How Much of the Earth Can You See at Once? which also covers this very subject.

How Much of the Earth Can You See at Once? by Vsauce. In the video, at 14:40, Michael says “You may have heard it said that if the entire planet were shrunk down to the size of a billiard ball, it would be smoother than it. … That seems believable, but as it turns out, it’s not true. The misconception stems from the interpretation of the World Pool-Billiard Association’s rules. According to them, a billiard ball must have a diameter of 2.25 in ±0.005 in. Some writers have taken this to mean that pits and bumps of ±0.005 in are allowed. Proportionally, on Earth, that would mean a mountain that was 28 km high. So, since Earth has none of those, it must be smoother than a billiard ball. Except, if bumps that high are actually allowed on a pool ball. A ball covered with 120-grit sandpaper would be within regulation. Clearly, the ±0.005 inches rule is more about roundness, deviation from a sphere, and not the texture.”

As you can see in the video above, as microscopic photography has shown, imperfections on a billiard ball are only 1/100,000 inches, or about 0.5 μm deep and high. Scaled down to the size of a billiard ball, Earth’s Mariana trench would be 49 μm deep.

What if we scale up a billiard ball to Earth-size?

Let’s think of it in another way: If a billiard ball was scaled up to Earth-size, the difference between the highest peak and lowest point would be about 223 meters (732 feet) at maximum. A billiard ball (or a cue ball, or a bowling ball, whatever) is way smoother than the Earth.

An image of Earth as a billiard ball. Despite being claimed by many reputable sources, the idea of Earth being as smooth as a billiard ball is a myth.
Despite being claimed by many “reputable” sources, the idea of Earth being as smooth as a billiard ball is a myth.

Sources

M. Özgür Nevres